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| # Please cite as: | |
| # Edossa, A. K., Schroeders, U., Weinert, S., & Artelt, C. (2018). | |
| # The development of emotional and behavioral self-regulation and their effects on academic | |
| # in childhood. International Journal of Behavioral Development, 42(2), 192–202. | |
| # https://doi.org/10.1177/0165025416687412 | |
| # | |
| # contact Ashenafi Kassahun Edossa <ashenafiedossa@gmail.com> | |
| # Ulrich Schroeders <ulrich.schroeders@gmail.com> | |
| # | |
| # title Longitudinal Measurement Invariance Testing with Categorical Data | |
| # GitHub https://github.com/ulrich-schroeders/syntax-publications | |
| # date 2015-08-04 | |
| # version 1.0.0 | |
| # Data availability statement: | |
| # The manuscript used data from the Millennium Cohort Study, which is a longitudinal birth cohort study that follows the lives of children born in 2000 and 2001 in the United Kingdom (more information: Hansen, K. (2014). Millennium cohort study first, second, third, fourth and fifth surveys: A guide to the datasets, (8th ed.). London: Centre for Longitudinal Studies, Institute of Education, University of London.). | |
| # Information and data set: https://discover.ukdataservice.ac.uk/series/?sn=2000031 | |
| # | |
| # Testing for Longitudinal Measurement Invariance with Continous and Categorical Data. | |
| # (more information in Edossa et al., 2018) | |
| # --------------------------------------------------------------------------- | |
| # Continuous Factor Residual Factor | |
| # variables Loadings Intercepts Variances Means | |
| # --------------------------------------------------------------------------- | |
| # Configural invariance * * * Fixed at 0 | |
| # Weak invariance Fixed * * Fixed at 0 | |
| # Strong invariance Fixed Fixed * Fixed at 0/* | |
| # Strict invariance Fixed Fixed Fixed Fixed at 0/* | |
| # | |
| # --------------------------------------------------------------------------- | |
| # Categorical variables Factor Tresholds Residual Factor | |
| # Loadings Variances Means | |
| # --------------------------------------------------------------------------- | |
| # Configural invariance (* *) Fixed at 1 Fixed at 0 | |
| # Strong invariance (Fixed Fixed) Fixed at 1/* Fixed at 0/* | |
| # Strict invariance (Fixed Fixed) Fixed at 1 Fixed at 0/* | |
| # --------------------------------------------------------------------------- | |
| # Note. The asterisk (*) indicates that the parameter is freely estimated. | |
| # Fixed = the parameter is fixed to equity over time points; Fixed at 1 = | |
| # the residual variances are fixed to 1 at all time points; Fixed at 0 = | |
| # factor means are fixed at 0 at all time points. Fixed at 0/* = factor | |
| # means are fixed at 0 at the first time point and freely estimated at the | |
| # other time points. Fixed at 1/* = the residual variances are fixed to 1 | |
| # at the first time point and freely estimated at the other time points. | |
| # Parameters in parentheses need to be varied in tandem. | |
| # Explanation of variable labels | |
| # ------------------------------ | |
| # er = emotional regulation | |
| # br = behavioral regulation | |
| # .x = age at which assessment took place | |
| library(lavaan) | |
| # configrual measurement invariance | |
| ----------------------------------- | |
| mod.configural <- ' | |
| # measurement part | |
| er.3 =~ er1.3 + er2.3 + er3.3 + er5.3 | |
| er.5 =~ er1.5 + er2.5 + er3.5 + er5.5 | |
| er.7 =~ er1.7 + er2.7 + er3.7 + er5.7 | |
| br.3 =~ isr4.3 + isr5.3 + task.3 + think.3 | |
| br.5 =~ isr4.5 + isr5.5 + task.5 + think.5 | |
| br.7 =~ isr4.7 + isr5.7 + task.7 + think.7 | |
| # mean structure | |
| er.3 ~ 0*1 | |
| er.5 ~ 0*1 | |
| er.7 ~ 0*1 | |
| br.3 ~ 0*1 | |
| br.5 ~ 0*1 | |
| br.7 ~ 0*1 | |
| # residual covariances | |
| er1.3 ~~ er1.5 + er1.7 | |
| er1.5 ~~ er1.7 | |
| er2.3 ~~ er2.5 + er2.7 | |
| er2.5 ~~ er2.7 | |
| er3.3 ~~ er3.5 + er3.7 | |
| er3.5 ~~ er3.7 | |
| er5.3 ~~ er5.5 + er5.7 | |
| er5.5 ~~ er5.7 | |
| isr4.3 ~~ isr4.5 + isr4.7 | |
| isr4.5 ~~ isr4.7 | |
| isr5.3 ~~ isr5.5 + isr5.7 | |
| isr5.5 ~~ isr5.7 | |
| think.3 ~~ think.5 + think.7 | |
| think.5 ~~ think.7 | |
| task.3 ~~ task.5 + task.7 | |
| task.5 ~~ task.7 ' | |
| fit.configural <- cfa(mod.configural, data=mcs, missing="pairwise", | |
| estimator="WLSMV", parameterization="theta", | |
| ordered =c("isr4.3", "isr4.5", "isr4.7", | |
| "isr5.3", "isr5.5", "isr5.7", | |
| "er1.3", "er1.5", "er1.7", | |
| "er2.3", "er2.5", "er2.7", | |
| "er3.3", "er3.5", "er3.7", | |
| "er5.3", "er5.5", "er5.7", | |
| "task.3", "task.5", "task.7", | |
| "think.3","think.5","think.7")) | |
| summary(fit.configural, fit.measures=TRUE, standardized=TRUE) | |
| # strong measurement invariance | |
| ------------------------------- | |
| mod.strong <- ' | |
| # measurement part | |
| er.3 =~ er1.3 + a2*er2.3 + a3*er3.3 + a4*er5.3 | |
| er.5 =~ er1.5 + a2*er2.5 + a3*er3.5 + a4*er5.5 | |
| er.7 =~ er1.7 + a2*er2.7 + a3*er3.7 + a4*er5.7 | |
| br.3 =~ isr4.3 + b2*isr5.3 + b3*task.3 + b4*think.3 | |
| br.5 =~ isr4.5 + b2*isr5.5 + b3*task.5 + b4*think.5 | |
| br.7 =~ isr4.7 + b2*isr5.7 + b3*task.7 + b4*think.7 | |
| # mean structure | |
| er.3 ~ 0*1 | |
| er.5 ~ NA*1 | |
| er.7 ~ NA*1 | |
| br.3 ~ 0*1 | |
| br.5 ~ NA*1 | |
| br.7 ~ NA*1 | |
| # thresholds | |
| er1.3 | c1*t1 + c2*t2; er1.5 | c1*t1 + c2*t2; er1.7 | c1*t1 + c2*t2 | |
| er2.3 | d1*t1 + d2*t2; er2.5 | d1*t1 + d2*t2; er2.7 | d1*t1 + d2*t2 | |
| er3.3 | e1*t1 + e2*t2; er3.5 | e1*t1 + e2*t2; er3.7 | e1*t1 + e2*t2 | |
| er5.3 | f1*t1 + f2*t2; er5.5 | f1*t1 + f2*t2; er5.7 | f1*t1 + f2*t2 | |
| isr4.3 | g1*t1 + g2*t2; isr4.5 | g1*t1 + g2*t2; isr4.7 | g1*t1 + g2*t2 | |
| isr5.3 | h1*t1 + h2*t2; isr5.5 | h1*t1 + h2*t2; isr5.7 | h1*t1 + h2*t2 | |
| task.3 | i1*t1 + i2*t2; task.5 | i1*t1 + i2*t2; task.7 | i1*t1 + i2*t2 | |
| think.3 | j1*t1 + j2*t2; think.5 | j1*t1 + j2*t2; think.7 | j1*t1 + j2*t2 | |
| # residual covariances | |
| er1.3 ~~ er1.5 + er1.7 | |
| er1.5 ~~ er1.7 | |
| er2.3 ~~ er2.5 + er2.7 | |
| er2.5 ~~ er2.7 | |
| er3.3 ~~ er3.5 + er3.7 | |
| er3.5 ~~ er3.7 | |
| er5.3 ~~ er5.5 + er5.7 | |
| er5.5 ~~ er5.7 | |
| isr4.3 ~~ isr4.5 + isr4.7 | |
| isr4.5 ~~ isr4.7 | |
| isr5.3 ~~ isr5.5 + isr5.7 | |
| isr5.5 ~~ isr5.7 | |
| think.3 ~~ think.5 + think.7 | |
| think.5 ~~ think.7 | |
| task.3 ~~ task.5 + task.7 | |
| task.5 ~~ task.7 | |
| # residual variances | |
| er1.3 ~~ 1*er1.3 | |
| er2.3 ~~ 1*er2.3 | |
| er3.3 ~~ 1*er3.3 | |
| er5.3 ~~ 1*er5.3 | |
| er1.5 ~~ NA*er1.5 | |
| er2.5 ~~ NA*er2.5 | |
| er3.5 ~~ NA*er3.5 | |
| er5.5 ~~ NA*er5.5 | |
| er1.7 ~~ NA*er1.7 | |
| er2.7 ~~ NA*er2.7 | |
| er3.7 ~~ NA*er3.7 | |
| er5.7 ~~ NA*er5.7 | |
| isr4.3 ~~ 1*isr4.3 | |
| isr5.3 ~~ 1*isr5.3 | |
| task.3 ~~ 1*task.3 | |
| think.3 ~~ 1*think.3 | |
| isr4.5 ~~ NA*isr4.5 | |
| isr5.5 ~~ NA*isr5.5 | |
| task.5 ~~ NA*task.5 | |
| think.5 ~~ NA*think.5 | |
| isr4.7 ~~ NA*isr4.7 | |
| isr5.7 ~~ NA*isr5.7 | |
| task.7 ~~ NA*task.7 | |
| think.7 ~~ NA*think.7 ' | |
| fit.strong<- cfa(mod.strong, data=mcs, missing="pairwise", | |
| estimator="WLSMV", parameterization="theta", | |
| ordered =c("isr4.3", "isr4.5", "isr4.7", | |
| "isr5.3", "isr5.5", "isr5.7", | |
| "er1.3", "er1.5", "er1.7", | |
| "er2.3", "er2.5", "er2.7", | |
| "er3.3", "er3.5", "er3.7", | |
| "er5.3", "er5.5", "er5.7", | |
| "task.3", "task.5", "task.7", | |
| "think.3","think.5","think.7")) | |
| summary(fit.strong, fit.measures=TRUE, standardized=TRUE) | |
| # strict measurement invariance | |
| ------------------------------- | |
| mod.strict <- ' | |
| # measurement part | |
| er.3 =~ er1.3 + a2*er2.3 + a3*er3.3 + a4*er5.3 | |
| er.5 =~ er1.5 + a2*er2.5 + a3*er3.5 + a4*er5.5 | |
| er.7 =~ er1.7 + a2*er2.7 + a3*er3.7 + a4*er5.7 | |
| br.3 =~ isr4.3 + b2*isr5.3 + b3*task.3 + b4*think.3 | |
| br.5 =~ isr4.5 + b2*isr5.5 + b3*task.5 + b4*think.5 | |
| br.7 =~ isr4.7 + b2*isr5.7 + b3*task.7 + b4*think.7 | |
| # mean structure | |
| er.3 ~ 0*1 | |
| er.5 ~ NA*1 | |
| er.7 ~ NA*1 | |
| br.3 ~ 0*1 | |
| br.5 ~ NA*1 | |
| br.7 ~ NA*1 | |
| # thresholds | |
| er1.3 | c1*t1 + c2*t2; er1.5| c1*t1 + c2*t2; er1.7 | c1*t1 + c2*t2 | |
| er2.3 | d1*t1 + d2*t2; er2.5| d1*t1 + d2*t2; er2.7 | d1*t1 + d2*t2 | |
| er3.3 | e1*t1 + e2*t2; er3.5| e1*t1 + e2*t2; er3.7 | e1*t1 + e2*t2 | |
| er5.3 | f1*t1 + f2*t2; er5.5| f1*t1 + f2*t2; er5.7 | f1*t1 + f2*t2 | |
| isr4.3 | g1*t1 + g2*t2; isr4.5 | g1*t1 + g2*t2; isr4.7 | g1*t1 + g2*t2 | |
| isr5.3 | h1*t1 + h2*t2; isr5.5 | h1*t1 + h2*t2; isr5.7 | h1*t1 + h2*t2 | |
| task.3 | i1*t1 + i2*t2; task.5 | i1*t1 + i2*t2; task.7 | i1*t1 + i2*t2 | |
| think.3 | j1*t1 + j2*t2; think.5 | j1*t1 + j2*t2; think.7 | j1*t1 + j2*t2 | |
| # residual covariances | |
| er1.3 ~~ er1.5 + er1.7 | |
| er1.5 ~~ er1.7 | |
| er2.3 ~~ er2.5 + er2.7 | |
| er2.5 ~~ er2.7 | |
| er3.3 ~~ er3.5 + er3.7 | |
| er3.5 ~~ er3.7 | |
| er5.3 ~~ er5.5 + er5.7 | |
| er5.5 ~~ er5.7 | |
| isr4.3 ~~ isr4.5 + isr4.7 | |
| isr4.5 ~~ isr4.7 | |
| isr5.3 ~~ isr5.5 + isr5.7 | |
| isr5.5 ~~ isr5.7 | |
| think.3 ~~ think.5 + think.7 | |
| think.5 ~~ think.7 | |
| task.3 ~~ task.5 + task.7 | |
| task.5 ~~ task.7 ' | |
| fit.strict<- cfa(mod.strict, data=mcs, missing="pairwise", | |
| estimator="WLSMV", parameterization="theta", | |
| ordered =c("isr4.3", "isr4.5", "isr4.7", | |
| "isr5.3", "isr5.5", "isr5.7", | |
| "er1.3", "er1.5", "er1.7", | |
| "er2.3", "er2.5", "er2.7", | |
| "er3.3", "er3.5", "er3.7", | |
| "er5.3", "er5.5", "er5.7", | |
| "task.3", "task.5", "task.7", | |
| "think.3","think.5","think.7")) | |
| summary(fit.strict, fit.measures=TRUE, standardized=TRUE) | |
| # testing the difference between the configural vs. strong MI model | |
| ------------------------------------------------------------------- | |
| anova(fit.configural, fit.strong, method="satorra.bentler.2010") |